Brady, the current chairman of the Joint Economic Committee, told columnist Al Hunt in an interview that will air Friday evening that he wants the top slot on the Ways and Means Committee, where he is currently the No. 2 Republican.

Reigning Chairman Dave Camp, R-Mich., must relinquish his title next year due to term limits.

"He's a terrific leader, a good friend," Brady said of Ryan, according to early transcript of a portion of the interview that will air on Bloomberg TV. "But the point is, I'm qualified and prepared to lead this committee. At the right time, I'm going to make that case to my colleagues. This is all about the ideas and how we can move tax reform, trade, entitlement reform forward, so it's good to have a healthy competition.

"I'm going to be in a position to lead this committee," Brady continued. "We'll see how all of it goes. ... Hopefully we're going to present two good choices."

Ryan's press office did not immediately return a request for comment.

Unlike the House Democratic Caucus , the House Republican Conference does not place as great a premium on seniority in doling out plum committee leadership assignments, though it does count for something. While Brady is No. 2 on the panel, Ryan comes in just after him at No. 3.

There's also a sense among House Republicans that because Ryan has a high profile and is well-liked, he can move into whatever job he wants, within reason. That could make any head-to-head race against him a challenge.